By taunting him.
Explanation:
Mercutio provoke a fight with Tybalt by taunting him. This taunting behaviour leads to fight between Mercutio and Tybalt. Prince not decided to have Romeo executed for his crimes because the prince have heard about Romeo's real part in the fight. The Prince might have heard Romeo tried to break it up and only got mad when Tybalt killed Mercutio unfairly and unnecessarily so the Prince take the right decision and his decision make sense.